Over the past decade, many findings in cognitive neuroscience have resulted in the view that selective attenti on, working memory and cognitive control involve competition between widely distributed rep- resentations. This competition is biased by top-down projections (notably from prefrontal cortex), which can selectively enhance some representations over others. This view has now been implemented in several connectionist models. In this review, we emphasize the relevance of these models to understanding con- sciousness. Interestingly, the models we review have striking similarities to others directly aimed at imple- menting ‘global workspace theory’. All of these models embody a fundamental principle that has been used in many connectionist models over the past twenty years: global constraint satisfaction.